U.S. patent application number 12/366552 was filed with the patent office on 2010-08-05 for prime-based frequency sampling.
This patent application is currently assigned to Sonora Medical Systems, Inc.. Invention is credited to Joseph Leo Valenti, III.
Application Number | 20100194377 12/366552 |
Document ID | / |
Family ID | 42397159 |
Filed Date | 2010-08-05 |
United States Patent
Application |
20100194377 |
Kind Code |
A1 |
Valenti, III; Joseph Leo |
August 5, 2010 |
PRIME-BASED FREQUENCY SAMPLING
Abstract
Various embodiments provide methods, apparatuses, and systems
for sampling a waveform using relatively prime sampling methods. A
waveform with a first plurality of cycles and a first frequency may
be sampled with a waveform sampling device. Sampling the waveform
may include sampling the waveform at a sampling rate of the
waveform sampling device. Sampling the waveform may include taking
a sample number of samples of the waveform where the sample number
may be relatively prime with respect to the number of cycles of the
waveform. The sample number of samples of the waveform may be
interleaved with a controller.
Inventors: |
Valenti, III; Joseph Leo;
(Longmont, CO) |
Correspondence
Address: |
STOEL RIVES LLP - SLC
201 SOUTH MAIN STREET, SUITE 1100, ONE UTAH CENTER
SALT LAKE CITY
UT
84111
US
|
Assignee: |
Sonora Medical Systems,
Inc.
Longmont
CO
|
Family ID: |
42397159 |
Appl. No.: |
12/366552 |
Filed: |
February 5, 2009 |
Current U.S.
Class: |
324/76.38 |
Current CPC
Class: |
G01R 13/0272
20130101 |
Class at
Publication: |
324/76.38 |
International
Class: |
G01R 13/34 20060101
G01R013/34 |
Claims
1. A method for sampling waveforms using relatively prime number
sampling, comprising: sampling, using a waveform sampling device, a
waveform with a first plurality of cycles and a first frequency,
wherein sampling the waveform includes: sampling at a first
sampling rate of the waveform sampling device; and sampling a first
sample number of samples of the waveform, wherein the first sample
number is relatively prime with respect to the first plurality of
cycles; and interleaving the first sample number of samples of the
waveform with a controller.
2. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein the first sample number is a prime
number.
3. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein the waveform sampling device is an
analog-to-digital converter.
4. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein the waveform sampling device is a
sound card coupled with a computer.
5. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein the waveform is dithered.
6. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein the first sample number is a function
of the first sampling rate and the first frequency.
7. The method for sampling waveforms using relatively prime number
sampling of claim 6, wherein the function is approximately an
inverse of a quotient of the first frequency and a product of a
first cycle number and a first sampling rate of the waveform
sampling device.
8. The method for sampling waveforms using relatively prime number
sampling claim 1, further comprising: sampling, with the waveform
sampling device, a second waveform with a second plurality of
cycles with a second frequency, wherein sampling the second
waveform includes: sampling at the first sampling rate of the
waveform sampling device; and sampling a second sample number of
samples of the second waveform, wherein the second sample number is
relatively prime with respect to the second plurality of full
cycles; and interleaving the second sample number of samples of the
second waveform with a controller.
9. The method for sampling waveforms using relatively prime number
sampling of claim 1, wherein sampling the waveform further
comprises sampling a waveform transmitted through a device under
test.
10. The method for sampling waveforms using relatively prime number
sampling of claim 9, further comprising determining a transfer
function for the device under test based on sampling the waveform
transmitted through the device under test.
11. The method for sampling waveforms using relatively prime number
sampling of claim 9, further comprising determining an impedance of
the device under test.
12. The method for sampling waveforms using relatively prime number
sampling of claim 9, further comprising determining a phase
shift.
13. A method for generating waveforms for sampling using relatively
prime number sampling, comprising: determining a relatively prime
sample number, wherein the relatively prime sample number is
relatively prime with respect to a cycle number; determining an
adjusted frequency, wherein the adjusted frequency is:
approximately equal to a test frequency; and a function of the
relatively prime sample number, the cycle number, and a sampling
rate of a waveform sampling device; and transmitting a waveform
with the adjusted frequency and the cycle number of cycles with a
waveform generating device.
14. The method for generating waveforms for sampling using
relatively prime number sampling of claim 13, wherein the function
approximately equals the inverse of a quotient of the relatively
prime sample number and a product of the cycle number and the
sampling rate.
15. The method for generating waveforms for sampling using
relatively prime number sampling of claim 13, wherein a user
determines the test frequency.
16. The method for generating waveforms for sampling using
relatively prime number sampling of claim 13, wherein the wave
generating device is a digital-to-analog converter.
17. The method for generating waveforms for sampling using
relatively prime number sampling of claim 16, wherein the
digital-to-analog converter is a sound card coupled with a
computer.
18 The method for generating waveforms for sampling using
relatively prime number sampling of claim 13, further comprising:
sampling, with a waveform sampling device, a second waveform with
the adjusted frequency and the cycle number of cycles, wherein
sampling the second waveform includes: sampling at the sampling
rate of the waveform sampling device; and sampling the second
waveform the relatively prime sample number of times; and
interleaving the relatively prime number of samples of the second
waveform with a controller.
19. The method for generating waveforms for sampling using
relatively prime number sampling of claim 18, wherein the waveform
is transmitted to a device under test and the second waveform is
received from the device under test.
20. A system for sampling waveforms using relatively prime number
sampling, comprising: a computational device; a waveform generating
device coupled with the computational device and configured to
transmit a first waveform with a plurality of cycles and a
frequency; and a waveform sampling device coupled with the
computational device and configured to sample a second waveform
with the plurality of cycles and the frequency a sample number of
times, wherein the sample number is relatively prime with respect
to the plurality of cycles.
21. The system for sampling waveforms using relatively prime number
sampling of claim 20, wherein the first waveform is transmitted to
a device under test from the waveform generating device and the
second waveform is received from the device under test at the
waveform sampling device.
22. A device for sampling waveforms using relatively prime number
sampling, comprising: means for sampling a waveform with a
plurality of cycles and a frequency, wherein sampling the waveform
includes: sampling at a sampling rate; and sampling a sample number
of samples of the waveform, wherein the sample number is relatively
prime with respect to the plurality of cycles; and means for
interleaving the sample number of samples of the waveform.
23. The device for sampling waveforms using relatively prime number
sampling of claim 22, further comprising: means for dithering the
sample number of samples of the waveform.
24. The device for sampling waveforms of claim 22, further
comprising: means for determining a relatively prime sample number,
wherein the relatively prime sample number is relatively prime with
respect to a cycle number; means for determining an adjusted
frequency, wherein the adjusted frequency approximately equals a
test frequency and is a function of the relatively prime sample
number, the cycle number, and a sample rate; and means for
transmitting a cycle number of cycles of a waveform with the
adjusted frequency.
Description
CROSS-REFERENCES TO RELATED APPLICATIONS
[0001] This application is related to the following commonly owned,
co-pending application, of which the entire disclosure is
incorporated herein, for all purposes, as if fully set forth
herein: U.S. patent application Ser. No. 12/337,317 filed on Dec.
17, 2008 by Valenti and entitled "Personal Computer Based Audio
Frequency Impedance Analyzer" (attorney docket no.
040100-000800US).
BACKGROUND OF THE INVENTION
[0002] This disclosure relates in general to methods, apparatuses,
and systems for generating and sampling waveforms using relatively
prime-based sampling techniques. Some embodiments involve device
under test ("DUT") analyzers and, but not by way of limitation,
audio frequency impedance analyzers among other things.
[0003] Some systems improve or increase the sampling rate by
increasing the frequency of sampling. For example, some devices may
have a sampling rate of 44.1 Kilohertz. One might instead use a
device with a higher sampling rate, such as one that may sample at
a rate over 1 Megahertz. Utilizing or developing a higher speed
sampler generally comes with a higher cost.
[0004] Some systems improve or increase the temporal resolution of
a sampling device using a digital storage oscilloscope utilizing
random interleaving sampling techniques. These systems require
significant amounts of time to work effectively.
[0005] There is a need for methods, apparatuses, and systems that
can improve the effective sampling rate and resolution capabilities
of waveform sampling devices.
BRIEF SUMMARY OF THE INVENTION
[0006] Various embodiments improve or increase the effective
sampling of a waveform using methods that include relatively prime
sampling techniques.
[0007] In one embodiment, a method for sampling a waveform using a
relatively prime sampling is provided. The waveform may have a
first plurality of cycles and a first frequency. The waveform may
be sampled with a waveform sampling device. Sampling the waveform
may include sampling the waveform at a sampling rate of a waveform
sampling device. Sampling the waveform may include taking a sample
number of samples of the waveform where the sample number may be
relatively prime with respect to the number of cycles of the
waveform. The sample number of samples of the waveform may be
interleaved with a controller.
[0008] In another embodiment, a method for generating waveforms for
sampling using relatively prime number sampling is provided. The
method may include determining a test frequency, a cycle number,
sample rate, and/or a relatively prime sample number. The
relatively prime sample number may be relatively prime with respect
to a cycle number. An adjusted frequency may be determined, where
the adjusted frequency approximately equals the test frequency. The
adjusted frequency may also be a function of a relatively prime
sample number, a cycle number, and a sampling rate. A waveform may
be transmitted with the adjusted frequency with the cycle number of
cycles using a waveform generating device.
[0009] In another embodiment, a system for sampling a waveform
using relatively prime sampling is provided. The system may include
a computational device. The system may include a waveform
generating device coupled with the computational device. The
waveform generating device may be configured to transmit a first
waveform. The first waveform may include a plurality cycles and a
frequency. The system may include a waveform sampling device
coupled with the computational device. The waveform sampling device
may be configured to receive a second waveform. The second waveform
may include the plurality of cycles and the frequency. The waveform
sample device may sample the second waveform at a sampling rate of
the wave sampling device. The waveform sampling device may sample
the second waveform a sample number of times, where the sample
number is relatively prime with respect to the plurality of
cycles.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving.
[0011] FIG. 2 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving.
[0012] FIG. 3 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving.
[0013] FIG. 4 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving involving a sampled reference
waveform and a sampled sense waveform.
[0014] FIG. 5 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving with waveforms with different
frequencies and amplitudes.
[0015] FIG. 6 provides a flow diagram illustrating a method for
sampling a waveform with relatively prime sampling.
[0016] FIG. 7 provides a flow diagram illustrating a method for
receiving and sampling a waveform with relatively prime
sampling.
[0017] FIG. 8A provides a structural diagram of embodiments
suitable for testing the response of a device under test ("DUT") to
a waveform using relatively prime sampling.
[0018] FIG. 8B provides a structural diagram of embodiments
suitable for testing the response of a DUT to a waveform using
relatively prime sampling.
[0019] FIG. 8C provides a structural diagram of embodiments
suitable for testing the response of a DUT to a waveform using
relatively prime sampling.
[0020] FIG. 9 provides a structural diagram of embodiments suitable
for testing the response of a DUT to a waveform using relatively
prime sampling.
[0021] FIG. 10 provides a schematic diagram of a computer used in
embodiments.
[0022] FIG. 11 provides diagrams of embodiments suitable for
sampling a waveform with a plurality of cycles with relatively
prime sampling and interleaving with waveforms with different
frequencies and amplitudes.
DETAILED DESCRIPTION OF THE INVENTION
[0023] The ensuing description provides exemplary embodiments only,
and is not intended to limit the scope, applicability or
configuration of the disclosure. Rather, the ensuing description of
the exemplary embodiments will provide those skilled in the art
with an enabling description for implementing one or more exemplary
embodiments, it being understood that various changes may be made
in the function and arrangement of elements without departing from
the spirit and scope of the invention as set forth in the appended
claims.
[0024] Specific details are given in the following description to
provide a thorough understanding of the embodiments. However, it
will be understood by one of ordinary skill in the art that the
embodiments may be practiced without these specific details. For
example, circuits, systems, networks, processes, and other elements
in the invention may be shown as components in block diagram form
in order not to obscure the embodiments in unnecessary detail. In
other instances, well-known circuits, processes, algorithms,
structures, and techniques may be shown without unnecessary detail
in order to avoid obscuring the embodiments.
[0025] Also, it is noted that individual embodiments may be
described as a process which is depicted as a flowchart, a flow
diagram, a data flow diagram, a structure diagram, or a block
diagram. Although a flowchart may describe the operations as a
sequential process, many of the operations can be performed in
parallel or concurrently. In addition, the order of the operations
may be re-arranged. A process may be terminated when its operations
are completed, but could have additional steps not discussed or
included in a figure. Furthermore, not all operations in any
particularly described process may occur in all embodiments. A
process may correspond to a method, a function, a procedure, a
subroutine, a subprogram, etc. When a process corresponds to a
function, its termination corresponds to a return of the function
to the calling function or the main function.
Overview of Embodiments
[0026] In one embodiment, a method for sampling a waveform using a
relatively prime sampling is provided. A waveform may include a
first plurality of cycles and a first frequency. The waveform may
be sampled with a waveform sampling device. Sampling the waveform
may include sampling the waveform at a first sampling rate of the
waveform sampling device. Sampling the waveform may include taking
a first sample number of samples of the waveform where the first
sample number may be relatively prime with respect to the first
plurality of cycles of the waveform.
[0027] In some embodiments, a first plurality of cycles may
represent the number of repetitions of a basic waveform that
comprise the waveform. Embodiments may include a plurality of
cycles where the cycles may be considered full cycles. In some
embodiments, a first frequency may be represented as a period of
the waveform. Some embodiments may include a plurality of cycles
where the cycles are full cycles.
[0028] In some embodiments, the waveform may be sampled with a
waveform sampling device where the waveform sampling device may
include a sound card, an audio card, an analog-to-digital converter
("ADC"), a network analyzer, a scalar analyzer, and/or a digital
storage oscilloscope. In some embodiments, the waveform sampling
device may sample the waveform at a sampling rate. In some
embodiments, a sound card or an audio card may be coupled with a
computer. The sampling rate may be determined by properties of the
waveform sampling device. Merely by way of example, a sound card
may have a sampling rate such as 22 Kilohertz (KHz), 44.1 KHz,
and/or 48 KHz. A sound card may also have higher or lower sampling
rates. Other waveform sampling devices, such as an ADC, may have
higher sampling rates. Merely by way of example, in some
embodiments, an ADC may have a sampling rate that is of the order
of magnitude of 10 KHz, 100 KHz, and/or 1,000 KHz. Some waveform
sampling devices may have even higher sampling rates, such as ones
with sampling rates of orders of magnitude of 10 Megahertz (MHz),
100 MHz, or 1,000 MHz), or even higher. Some waveform sampling
devices may have lower sampling rates, such as ones with sampling
rates, merely by way of example, below 22 KHz.
[0029] In some embodiments, a first sample number may be a
relatively prime number with respect to a cycle number. In some
embodiments, a first sample number may be a prime number. In some
embodiments, a sample number relatively prime with respect to a
cycle number may mean that the sample number and the cycle number
share only one positive common integer divisor, that being the
number 1. In some embodiments, a sample number may be relatively
prime with respect to a number representing the repetition found
within a waveform.
[0030] In some embodiments, a first sample number may be a function
of a sampling rate and a frequency. In some embodiments, a sampling
rate may be a first sampling rate of a waveform receiving device.
In some embodiments, a frequency may be a first frequency of the
waveform being sampled. Merely by way of example, a function
representing a sample number (or a number of samples, or in some
embodiments, a Minimum Number of Points ("MNOP")), may be
represented with the following equation for some embodiments based
on a cycle number (or a number of cycles), and a frequency of the
waveform and a sample rate of the waveform sampling device:
Sample_Number = Cycle_Numer .times. Sample_Rate Frequency .
##EQU00001##
In some embodiments, a frequency may be determined using a
relatively prime sample number (or a number of samples, or
sometimes represented as a MNOP), a cycle number (or a number of
cycles), and sample rate using an equation based on such a sample
number equation:
Frequency = Cycle_Number .times. Sample_Rate Relatively_Prime
_Sample _Number . ##EQU00002##
[0031] In some embodiments, the samples taken of a waveform may be
interleaved to represent a sampling of a cycle of the waveform with
a higher resolution. In some embodiments, the resolution may
represent a higher effective sampling rate. In some embodiments,
the effective sampling rate may be approximately equal to a product
of the first sampling rate and the number of cycles, or the first
plurality of cycles, of the waveform. In some embodiments,
interleaving may involve taking samples from each cycle of the
plurality of cycles and interleaving them. In some embodiments,
interleaving may be achieved by determining an integer position in
a data array using the following equation:
Position = Truncate ( M N O P .times. FractionalPart (
Sample_Position .times. Cycle_Number M N O P ) ) , ##EQU00003##
where MNOP may be a Minimum Number of Points or, in some
embodiments, a relatively prime sample number (or a relatively
prime number of samples) taken of a waveform, sample position may
be a number representing the position of a sample of the waveform,
cycle number (or a number of cycles) may be the number of cycles
within the waveform being sampled, and relatively prime sample
number may be a number of samples taken of a waveform that is
relatively prime with respect to the cycle number.
[0032] In some embodiments, interleaving may be done with a
controller. A controller may be a variety of devices or components.
Merely by way of example, a controller may be or involve a
computer, a sampling device, a network analyzer, a scalar analyzer,
a digital storage oscilloscope, and/or other devices capable of
interleaving samples of a sampling device. One skilled in the art
will recognize that interleaving may be achieved by many devices,
not limited to the those disclosed.
[0033] In some embodiments, a waveform being sampled with a
waveform sampling device may be dithered. For some embodiments,
dithering a waveform may include adding random noise to each sample
of the waveform. In some embodiments, dithering may be an
intentionally applied form of noise, used to randomize quantization
error, thereby preventing large-scale patterns such as contouring
that are more objectionable than uncorrelated noise. In some
embodiments, dithering may occur before the waveform is sampled by
the waveform sampling device.
[0034] In some embodiments, a waveform being sampled by a waveform
sampling device may be fitted using least square fitting techniques
well known in the art.
[0035] In some embodiments, a waveform sampling device may sample
more than one waveform using relatively prime sampling methods. In
some embodiments, a waveform sampling device may sample a train of
waveforms, where the waveforms are separated by time periods. In
some embodiments, a waveform may thus comprise a plurality of
waveforms, where each of the plurality of waveforms may have a
different plurality of cycles. In some embodiments, the plurality
of waveforms may have the same number of cycles. In some
embodiments, the plurality of waveforms may have different
frequencies or amplitudes. In some embodiments, the plurality of
waveforms may be sampled at the same sampling rate. In some
embodiments, the plurality of waveforms may be sampled at different
sampling rates. In some embodiments, the plurality of waveforms may
each be sampled a different number of sample times. In some
embodiments, the sample number may be the same for each of the
plurality of waveforms. In some embodiments, the sample numbers may
be relatively prime with respect to the number of cycles in the
waveform being sampled. Equations for a sample number or a
frequency may be determined in analogy with the equations given for
an embodiment with a first waveform and a first sampling number as
disclosed in this Application.
[0036] In some embodiments, a waveform sampled using relatively
prime sampling methods may have been transmitted through a device
under test ("DUT"). Merely by way of example, co-pending
application U.S. patent application Ser. No. 12/337,317 filed on
Dec. 17, 2008 by Valenti and entitled "Personal Computer Based
Audio Frequency Impedance Analyzer" provides apparatuses, systems,
and methods that may be used with relatively prime sampling
techniques involving DUTs for some embodiments. For some
embodiments, sampling a waveform using relatively prime sampling
methods may also include determining a transfer function for a DUT.
Some embodiments may determine an impedance of a DUT. Some
embodiments may determine a phase shift of a waveform. Some
embodiments may determine an amplitude change of a waveform.
[0037] In another embodiment, a method for generating waveforms for
sampling using relatively prime number sampling is provided. The
method may include determining a test frequency, a cycle number, a
sample number, sample rate, and/or a relatively prime sample
number. The relatively prime sample number may be a relatively
prime number with respect to a cycle number. An adjusted frequency
may be calculated with a computational device, where the adjusted
frequency approximately equals the test frequency. The adjusted
frequency may also be a function of a relatively prime sample
number, a cycle number, and a sampling rate. A waveform may be
transmitted with the adjusted frequency with the cycle number of
cycles using a waveform generating device.
[0038] In some embodiments, a test frequency may be determined by a
user. In some embodiments, multiple test frequencies may be
determined. In some embodiments, a test frequency may be
predetermined. In some embodiments, a test frequency may be
determined by a computational device. In some embodiments, a test
frequency may be determined by a waveform generating device.
[0039] In some embodiments, a cycle number may be determined by a
user. In some embodiments, a cycle number may be an integer greater
than one. In some embodiments, multiple cycle numbers may be
determined. In some embodiments, a cycle number may be
predetermined. In some embodiments, a cycle number may be
determined with a computational device. In some embodiments, a
cycle number may be determined with a waveform generating
device.
[0040] In some embodiments, a sample number may be determined by a
user. In some embodiments, multiple sample numbers may be
determined. In some embodiments, a sample number may be
predetermined. In some embodiments, a sample number may be
determined with a computational device. In some embodiments, a
sample number may be determined with a waveform generating
device.
[0041] In some embodiments, a relatively prime sample number may be
relatively prime with respect to a cycle number. In some
embodiments, a relatively prime sample number may be a prime
number. In some embodiments, a relatively prime sample number may
be determined by a user. In some embodiments, multiple relatively
prime samples numbers may be determined. In some embodiments, a
relatively prime sample number may be predetermined. In some
embodiments, a relatively prime sample number may be determined
with a computational device. In some embodiments, a relatively
prime sample number may be determined with a waveform generating
device.
[0042] In some embodiments, an adjusted frequency may be calculated
and/or determined. In some embodiments, an adjusted frequency may
be determined by a user. In some embodiments, multiple adjusted
frequencies may be determined. In some embodiments, an adjusted
frequency may be predetermined. In some embodiments, an adjusted
frequency may be determined with a computational device. In some
embodiments, an adjusted frequency may be determined with a
waveform generating device. In some embodiments, an adjusted
frequency approximately equals a test frequency. In some
embodiments, an adjusted frequency may be a function of a
relatively prime sample number, a cycle number, and a sampling
rate. In some embodiments, an adjusted frequency may be calculated
by an equation similar to the following using a cycle number ( or
number of cycles) of a waveform, a sampling rate of a waveform
sampling device, and a relatively prime sample number (or
relatively prime number of samples or in some embodiments, a MNOP)
which may represent the number of samples to be taken of a waveform
that is relatively prime with respect to the cycle number:
Adjusted_Frequency = Cycle_Number .times. Sample_Rate
Relatively_Prime _Sample _Number . ##EQU00004##
[0043] In some embodiments, a waveform may be transmitted with the
adjusted frequency with the cycle number of cycles using a waveform
generating device. In some embodiments, a waveform generating
device may include a sound card, an audio card, an
digital-to-analog converter ("DAC"), a network analyzer, a scalar
analyzer, and/or a digital storage oscilloscope, or other well
known waveform generating devices. In some embodiments, a waveform
generating device may be coupled with a computer.
[0044] In some embodiments, a waveform generating device may be
coupled with a DUT, such that the waveform generating device may
transmit a waveform to a DUT. In some embodiments, a waveform
transmitted through a DUT may be used to provide measures of the
DUT, such as the response of the DUT to the waveform. In some
embodiments, a waveform representing a response of a DUT may be
used to determine a transfer function, an impedance, a phase shift,
an amplitude change, and/or other measures of the DUT.
[0045] In some embodiments, the waveform sampling device may sample
the waveform at a sampling rate that may be transmitted from a
waveform generating device. Some embodiments will sample a second
waveform that is different from a first waveform transmitted from a
waveform generating device. In some embodiments, the first waveform
and the second waveform may be the same waveform. In some
embodiments, a waveform generating device may be coupled with a
computer. A waveform sampling device may sample the second waveform
a relatively prime sample number of times. Some embodiments may
interleave a relatively prime sample number of samples using a
controller. A controller may be a variety of devices or components.
Merely by way of example, a controller may be or include a
computer, a sampling device, a network analyzer, a scalar analyzer,
a digital storage oscilloscope, and/or other devices/components
capable of interleaving samples of a sampling device.
[0046] In another embodiment, a system for sampling a waveform
using relatively prime sampling is provided. The system may include
a computational device. The system may include a waveform
generating device. The waveform generating device may couple with a
computational device. The waveform generating device may be
configured to transmit a waveform. The waveform may be a first
waveform that may include a plurality of cycles at a frequency. The
plurality of cycles at a frequency may coincide with a first sample
number. The system may include a waveform sampling device. The
waveform sampling device may couple with a computational device.
The waveform sampling device may be configured to receive a
waveform. The waveform may be a second waveform that includes the
plurality of cycles at the frequency. The waveform sampling device
may sample the waveform at a sampling rate of the waveform sampling
device. The waveform sampling device may sample the waveform a
sample number of times, where the sample number is relatively prime
with respect to the plurality of cycles. The waveform sampling
device and the waveform generating device may be components of
another device, such as a network analyzer, scalar analyzer, or a
computer, merely by way of example. In some embodiments, a first
waveform may be transmitted to a device under test ("DUT") from the
waveform generating device and then received by the waveform
sampling device after the waveform has passed through the DUT. In
some embodiments, a waveform transmitted from the waveform
generating device may pass to the waveform sampling device without
passing through a DUT. In some embodiments, samples of a waveform
that passes through a DUT and a waveform that does not pass through
a DUT may be compared to determine different measures of the DUT,
such as a transfer function, an amplitude shift, a phase shift, or
other measures of the DUT.
[0047] In another embodiment, a device for sampling waveforms using
relatively prime sampling is provided. The device for sampling
waveforms using relatively prime sampling may include a sampling
means for sampling a waveform where the waveform has a plurality of
cycles and a frequency. Sampling the waveform may include sampling
at a sampling rate. Sampling of the waveform may include sampling a
sample number of samples of the waveform, where the sample number
is relatively prime with respect to the plurality of cycles.
[0048] In some embodiments of a device for sampling waveforms using
relatively prime sampling, a sampling means may include a sound
card, an audio card, an analog-to-digital converter ("ADC"), a
network analyzer, a scalar analyzer, and/or a digital storage
oscilloscope. In some embodiments, the sampling means may sample
the waveform at a sampling rate of a sound card, an audio card, an
analog-to-digital converter ("ADC"), a network analyzer, a scalar
analyzer, and/or a digital storage oscilloscope. In some
embodiments, a sound card or audio card may be coupled with a
computer. The sampling rate may be determined by properties of the
receiving means. Merely by way of example, a sound card may have a
sampling rate such as 22 Kilohertz (KHz), 44.1 KHz, and/or 48 KHz.
A sound card may also have higher or lower sampling rates. Other
sampling means, such as an ADC, may have higher sampling rates.
Merely by way of example, in some embodiments, an ADC or other
waveform sampling device may have a sampling rate that is of the
order of magnitude of 10 KHz, 100 KHz, 1,000 KHz. Some sampling
means may have even higher sampling rates, such as ones with
sampling rates of orders of magnitude of 10 Megahertz (MHz), 100
MHz, or 1,000 MHz, or even higher. Some waveform sampling devices
may have lower sampling rates, such as ones with sampling rates,
merely by way of example, below 22 KHz.
[0049] In some embodiments, a device for sampling waveforms using
relatively prime sampling may include means for dithering samples
of a waveform. Dithering means may include adding random noise to
each sample of the waveform. In some embodiments, dithering may be
an intentionally applied form of noise, used to randomize
quantization error, thereby preventing large-scale patterns such as
contouring that are more objectionable than uncorrelated noise. In
some embodiments, dithering may occur before the waveform is
sampled by the waveform receiving device.
[0050] In some embodiments, a device for sampling waveforms using
relatively prime sampling may include means for determining a
relatively prime sample number that may be relatively prime with
respect to a cycle number. A means for determining a relatively
prime sample number may involve calculating the relatively prime
sample number. A means for determining a relatively prime sample
number may determine a prime number. A means for determining a
relatively prime sample number may be with a computational device.
A means for determining a relatively prime sample number may be
with a waveform generating device or a waveform sampling device. A
means for determining a relatively prime sample number may be
determined by a user. In some embodiments, a means for determining
a relatively prime sample number may determine multiple relatively
prime sample numbers. A means for determining a relatively prime
sample number may be predetermined.
[0051] In some embodiments, a means for determining an adjusted
frequency may be calculated and/or determined. A means for
determining a relatively prime sample number may involve
calculating the adjusted frequency. In some embodiments, a means
for determining an adjusted frequency may be determined by a user.
In some embodiments, multiple adjusted frequencies may be
determined. In some embodiments, an adjusted frequency may be
predetermined. In some embodiments, a means for determining an
adjusted frequency may be calculated or determined with a
computational device. In some embodiments, a means for determining
an adjusted frequency may be calculated or determined with a
waveform generating device. In some embodiments, an adjusted
frequency approximately equals a test frequency. In some
embodiments, a means for determining an adjusted frequency may be
calculated or determined by a user. In some embodiments, an
adjusted frequency may be a function of a relatively prime sample
number, a cycle number, and a sampling rate. In some embodiments,
an adjusted frequency may be calculated by an equation similar to
the following using a cycle number (or number of cycles) of a
waveform, a sampling rate of a waveform sampling device, and a
relatively prime sample number (or relatively prime number of
samples or in some embodiments, a MNOP), which may represent the
number of samples to be taken of a waveform that is relatively
prime with respect to the cycle number:
Adjusted_Frequency = Cycle_Number .times. Sample_Rate
Relatively_Prime _Sample _Number . ##EQU00005##
[0052] In some embodiments, a device for sampling waveforms may
include a means for transmitting a waveform with an adjusted
frequency with a cycle number of cycles using a waveform generating
device. In some embodiments, a means for transmitting may be a
sound card, an audio card, an digital-to-analog converter ("DAC"),
a network analyzer, a scalar analyzer, and/or a digital storage
oscilloscope, or other well known waveform transmitting devices. In
some embodiments, a means for transmitting may be coupled with a
computer.
[0053] In some embodiments, a means for transmitting may be coupled
with a DUT, such that the waveform generating device may transmit a
waveform to a DUT. In some embodiments, a waveform transmitted
through a DUT may be used to provide measures of the DUT, such as
the response of the DUT to the waveform. In some embodiments, a
waveform representing a response of a DUT may be used to determine
a transfer function, an impedance, a phase shift, an amplitude
change, and/or other measures of the DUT.
[0054] Turning now to the figures, embodiments provide apparatuses,
systems, and methods for sampling a waveform using relatively prime
sampling methods. Such apparatuses, systems, and methods may
include receiving a waveform 110 such as that seen in FIG. 1, which
provides an overview of relatively prime sampling.
[0055] FIG. 1 provides waveform 110, which includes two cycles of a
base waveform represented by base waveform 120 and base waveform
130, which are the same in shape. Waveforms 110, 120, and 130 may
also have the same frequency. Samples of waveform 110 such as 111
and 112 may be taken as waveform 110 is sampled by a waveform
receiving and/or sampling device. Merely by way of example,
resulting waveform 150 may be produced by interleaving samples of
waveform 110 such as 111 and 112. In resulting waveform 150, sample
151 may correspond with sample 111 and sample 152 corresponds to
sample 112. In some embodiments, the samples taken of waveform 110
may be interleaved as shown with interleaving pattern 180. Other
embodiments may provide other interleaving patterns. FIG. 1
provides an embodiment where the number of samples, or sample
number, 170 sampled of waveform 110 is relatively prime with
respect to the number of cycles, or cycle number, 160 within
waveform 110. In some embodiments, sample number 170 may be a prime
number. Merely by way of example, sample number 170 in this case is
the number 23, while cycle number 160 is the number 2. These two
numbers are relatively prime with respect to each other as the only
positive common integer divisor the two numbers share is the number
1. In general, relatively prime sampling apparatuses, systems, and
methods may work where the cycle number is at least two. In some
embodiments, the cycle number may be two. In other embodiments, the
cycle number may take on numerous other values, as long as the
cycle number may be at least two. Merely by way of example, a cycle
number may be orders of magnitude larger than those shown here,
such as from 10, to 100, to 1000, to 10,000, times larger, and
possibly even larger. Furthermore, the sample number may be orders
of magnitude larger than shown in these embodiments. Merely by way
of example, a sample number may be orders of magnitude larger,
merely by way of example, from 10, 1000, 10000, or 100000 times
larger, or even larger, than the embodiments shown here.
Furthermore, in general, a cycle number and a sample may be
relatively prime with respect to each other with relatively prime
sampling methods, apparatuses, and systems.
[0056] FIG. 2 provides another embodiment where waveform 210
includes three cycles of a base waveform represented by base
waveforms 220, 230, and 240, which are the same in shape. Waveforms
210, 220, 230, and 240 may have the same frequency. Samples of
waveform 210 such as 211, 212, and 213 may be taken as waveform 210
is sampled by a waveform receiving and/or sampling device. Merely
by way of example, resulting waveform 250 may be produced by
interleaving samples of waveform 210 such as 211, 212, and 213. In
resulting waveform 250, sample 251 may correspond with sample 211,
sample 252 may correspond with sample 212, and sample 253
corresponds to sample 213. In some embodiments, the samples taken
of waveform 210 may be interleaved as shown with interleaving
pattern 280. Other embodiments may provide other interleaving
patterns. FIG. 2 provides an embodiment where the number of
samples, or sample number, 270 sampled of waveform 210 is
relatively prime with respect to the number of cycles, or cycle
number, 260 within waveform 210. In some embodiments, sample number
270 may be a prime number. Merely by way of example, sample number
270 in this case is the number 23, while cycle number 160 is the
number 3. These two numbers are relatively prime with respect to
each other as the only positive common integer divisor the two
numbers share is the number 1. In general, relatively prime
sampling apparatuses, systems, and methods may work where the cycle
number is at least two. In some embodiments, the cycle number may
be three. In other embodiments, the cycle number may take on
numerous other values greater than the number 1. Furthermore, in
general, a cycle number and a sample may be relatively prime with
respect to each other with relatively prime sampling methods,
apparatuses, and systems.
[0057] FIG. 3 provides another embodiment where waveform 310
includes two cycles of a base waveform represented by base waveform
320 and base waveform 330, which are the same in shape. Waveforms
310, 320, and 330 may have the same frequency or period. Samples of
waveform 310 such as 311 and 312 may be taken as waveform 310 is
sampled by a waveform receiving and/or sampling device. Merely by
way of example, resulting waveform 350 may be produced by
interleaving samples of waveform 310 such as 311 and 312. In
resulting waveform 350, sample 351 may correspond with sample 311
and sample 352 corresponds to sample 312. In some embodiments, the
samples taken of waveform 310 may be interleaved as shown within
resulting waveform 350. Other embodiments may provide other
interleaving patterns. FIG. 3 provides an embodiment where the
number of samples, or sample number, 370 sampled of waveform 310 is
relatively prime with respect to the number of cycles, or cycle
number, 360 within waveform 310. In some embodiments, sample number
370 may be a prime number. Merely by way of example, sample number
370 in this case is the number 25, while cycle number 360 is the
number 2. These two numbers are relatively prime with respect to
each other as the only positive common integer divisor the two
numbers share is the number 1. In this embodiment, sample number
370 does not have to be a prime number. Rather, this embodiment
shows that a sample number may be relatively prime with respect to
a cycle number without the sample number having to be a prime
number. In general, relatively prime sampling apparatuses, systems,
and methods may work where the cycle number may be at least two. In
some embodiments, the cycle number may be two. In other
embodiments, the cycle number may take on numerous other values.
Furthermore, in general, a cycle number and a sample may be
relatively prime with respect to each other with relatively prime
sampling methods, apparatuses, and systems.
[0058] FIG. 4 provides embodiments where a waveform 420 used for
relatively prime sampling may be affected in some way, resulting in
it being transformed into another waveform 430. In some
embodiments, waveform 430 results from a waveform like 420 passing
through a device under test ("DUT"). In some embodiments, waveform
420 may represent a waveform associated with a reference channel
410. In some embodiments, waveform 430 may represent a waveform
associated with a sense channel 415. In some embodiments, waveform
420 represents a waveform that may be transmitted from a waveform
generating device. In some embodiments, waveform 420 may represent
a waveform that has passed through circuitry excluding a DUT. FIG.
4 shows the amplitudes of the waveforms along a vertical axis 440.
Two horizontal axes 440 and 450 generally represent a time
dimension. In addition, FIG. 4 provides embodiments where waveforms
such as 420 and 430 may be preceded by timing waveforms 425 and
435, which may be used to help synchronize or otherwise coordinate
data that is captured when a waveform such as 420 or 430 is sampled
using relatively prime sampling methods, apparatuses, and
systems.
[0059] FIG. 5 provides embodiments where a waveform for relatively
prime sampling may include a train of waveforms, where each part of
the train of waveforms may have different amplitudes, frequencies,
cycle numbers, and/or sample numbers. Waveform train 510 may
represent a waveform including: a first waveform 520 with a first
frequency, a first amplitude, a first cycle number, and a first
sample number; second waveform 521 with a second frequency, a
second amplitude, a second cycle number, and a second sample
number; and a third waveform 522 with a third frequency, a third
amplitude, a third cycle number, and a third sample number.
Waveform train 510 may be altered in some way, such as if it were
to pass through a DUT, resulting in some embodiments in another
waveform train 515. Waveform train 515 may represent a waveform
including: a fourth waveform 530 with the first frequency, a fourth
amplitude, the first cycle number, and the first sample number;
fifth waveform 531 with the second frequency, a fifth amplitude,
the second cycle number, and the second sample number; and a sixth
waveform 532 with the third frequency, a sixth amplitude, the third
cycle number, and the third sample number. As seen with FIG. 4,
FIG. 5 includes vertical axis 540 representing amplitude of the
waveforms and horizontal axes 550 and 560 representing time. Some
embodiments may include more or less waveforms within their train
of waveforms.
[0060] While embodiments disclosed within FIGS. 1, 2, 3, 4, and 5
generally disclose waveforms representing sine waves, other
waveforms may be used in other embodiments. For example, waveforms
represent square waveforms, sawtooth waveforms, ramp waveforms, or
other well-known waveforms may be used. Furthermore, in some
embodiments, a waveform used for relatively prime-based sampling
may be generated utilizing a base waveform comprising many
frequencies thus representing a complicated waveform. In such
embodiments, methods, apparatuses, and systems utilizing relatively
prime based sampling may still be used where the embodiment
generates an overall waveform that includes two or more copies, or
cycles, of the complicated base waveform and the number of copies,
or cycle number, of the complicated base waveform may be relatively
prime with respect to the number of samples taken of the overall
waveform. FIG. 11 provides embodiments where the waveform 1100
comprises multiple cycles of a more complicated base waveform,
shown as 1120, 1130, 1140, and 1150, that may be sampled using
relatively prime sampling to represent a resulting waveform 1160.
As one skilled in the art will recognize, FIGS. 1, 2, 3, 4, 5, and
11 may show idealized waveforms; actual waveforms used with
embodiments of relatively prime sampling may include noise and
other distortions making them deviate from idealized waveforms.
Methods
[0061] In some embodiments, methods may be provide for sampling a
waveform using relatively prime sampling methods. Some embodiments
may be used for testing the response of a DUT to a waveform using
stimulus and response techniques. Stimulus and response techniques
may be used to measure both calibration and DUT measure functions.
An overview of embodiments suitable for methods involving
relatively prime sampling is provided in the flow diagram of FIG.
6.
[0062] At block 605, a test frequency of a waveform may be
determined. In some embodiments, the test frequency may be provided
by a user. The test frequency may also be predetermined or provided
by another source such as a computational device or waveform
generating and/or sampling device, merely by way of example. The
test frequency may be represented as a period of the waveform in
some embodiments. A period in general is inversely related to a
frequency. More than one test frequency may be determined. For
example, a user may provide a series of test frequencies to be used
in analyzing the response of a DUT. Along with determining at least
one test frequency at block 605, amplitudes for each waveform may
also be determined. As with the test frequency, the amplitude may
be determined by a user or may be predetermined or may be provided
by another source. At block 605, other details regarding a test
waveform with a test frequency may also be determined. Merely by
way of example, the shape of the waveform with a test frequency may
also be determined. For example, a waveform may comprise sine
waves, square waves, sawtooth waves, or any one of numerous well
known waveforms. In some embodiments, a complicated waveform may be
created that is a composition of other waveforms.
[0063] At block 610, a sample rate may be determined. A sample rate
may also be referred to as a sampling rate. A sample rate may be
provided by a user. The sample rate may also be predetermined or
provided by another source such as a computational device or
waveform generating and/or sampling device, merely by way of
example. The sample rate may be determined by the properties of a
waveform sampling device. Merely by way of example, a waveform
sampling device such as a sound card attached to a computer may
have a sample rate such as 44.1 Kilohertz, or 48 Kilohertz, or
other possible sample rates. Some waveform sampling devices, such
as some analog-to-digital converters, may have higher or lower
sample rates.
[0064] At block 615, a cycle number may be determined. A cycle
number may be a number of base waveforms at a test frequency. A
cycle number may represent the repetition within a waveform. A
general waveform may comprise a number of copies of a base
waveform, wherein the number of copies may be the cycle number. In
general, a cycle number may refer to a total number of complete
cycles of a test waveform at a test frequency. A cycle number may
be determined for each test frequency if there is more than one
test frequency. Cycle numbers may be provided by a user. Cycle
numbers may also be predetermined or provided by another source,
such as a computational device or waveform generating and/or
sampling device, merely by way of example.
[0065] At block 620, a sample number may be determined. A sample
number may be the number of samples comprising a test waveform with
a cycle number at a test frequency. A sample number may be
determined for each test frequency. A sample number may be provided
by a user. A sample number may be predetermined or provided by
another source, such as a computational device or waveform
generating and/or sampling device, merely by way of example.
[0066] At block 625, a relatively prime sample number may be
determined. A relatively prime sample number may be determined for
each sample number determined at block 620. A relatively prime
sample number may be a sample number that is a relatively prime
number with respect to a cycle number determined in block 615. Two
different numbers are relatively prime with respect to each other
when their only positive common integer divisor is the number 1. In
some embodiments, a relatively prime sample number may be
approximately a sample number determined in block 620. A relatively
prime sample number may be the relatively prime number with respect
to a cycle number from block 615 that is closest to a sample number
from block 620. In some embodiments, a relatively prime sample
number may be a prime number. In some embodiments, a user may
provide a relatively prime sample number. In some embodiments, a
relatively prime sample number may be calculated or determined with
a computer or other device, such as a computational device or
waveform generating and/or sampling device, merely by way of
example. In some embodiments, a relatively prime sample number be
determined by other well known techniques, such as from a table of
numbers. In some embodiments, a relatively prime sample number may
be predetermined.
[0067] At block 630, a test frequency determined in block 605 may
be adjusted. A test frequency may be adjusted in order that the
length of a waveform at the adjusted test frequency coincides with
the relatively prime sample number. Merely by way of example, an
adjusted test frequency may be determined in some embodiments such
that:
Test_Frequency = Cycle_Number .times. Sample_Rate Relatively_Prime
_Sample _Number , ##EQU00006##
where the cycle number (or number of cycles) may be determined in
block 615, the sample rate may be determined in block 610, and the
relatively prime sample number (or relatively prime number of
samples or in some embodiments, a MNOP) may be determined in block
625. In some embodiments, a cycle number determined in block 615, a
sample number determined in block 610, and a relatively prime
sample number determined in block 625, may be individually or
collectively adjusted in order that the adjusted test frequency
determined in block 630 is approximately a test frequency
determined in block 605.
[0068] It will be recognized that the order of these blocks 605,
610, 615, 620, 625, and 630 may occur in different orders. In some
embodiments, not all the blocks will be used within a given method
embodiment.
[0069] At block 635, a test waveform may be generated using a
waveform generating device. A test waveform may be transmitted
where the test waveform includes a cycle number of base waveforms
at an adjusted test frequency. In some embodiments, an overall test
waveform may include a plurality of test waveforms, where each test
waveform comprises possibly a different cycle number of cycles of a
possibly different base waveform at a possibly different adjusted
test frequency. In some embodiments, a sound card coupled with a
computer may transmit a generated test waveform. Other waveform
generating devices may also be used. For example, a network
analyzer, a scalar analyzer, a general digital-to-analog converter,
or a function generator may be used. Other devices capable of
generating a waveform may also be used. Merely by way of example, a
test waveform based on a sine wave may be generated using an
equation such as the following that produces amplitudes of test
waveform based on a specific sample position, where a specific
sample position may range from zero to a relatively prime sample
number (or relatively prime number of samples or MNOP) that may be
determined in block 625, a cycle number (or number of cycles), the
relatively prime sample number (or relatively prime number of
samples or MNOP), and a constant C:
Amplitude = C .times. Sin ( 360 .degree. .times. FractionalPart (
Sample_Position .times. Cycle_Number Relatively_Prime _
Sample_Number ) ) . ##EQU00007##
[0070] At block 640, a test waveform generated at block 635 may be
transmitted through a DUT. Merely by way of example, a test
waveform may be transmitted to a DUT using a Z box as disclosed in
co-pending application U.S. patent application Ser. No. 12/337,317
filed on Dec. 17, 2008 by Valenti and entitled "Personal Computer
Based Audio Frequency Impedance Analyzer." At block 645, a test
waveform generated at block 635 may also be transmitted without
passing through a DUT. In some embodiments, a test waveform that
may not be transmitted through a DUT may be used as a reference
waveform that may be used for calibration purposes. In some
embodiments, a test waveform that may not betransmitted through a
DUT may also be used to determine different measures of the DUT
when compared with a test waveform that passes through a DUT. In
some embodiments, measures of a DUT may include a transfer
function, an impedance, a phase shift, an amplitude, and/or other
measures of the DUT.
[0071] At block 650, test waveforms may be received by a waveform
sampling device. In some embodiments, the test waveforms may be
received by a sound card. In some embodiments, a waveform receiving
device may be an analog-to-digital converter ("ADC"). In some
embodiments, a waveform receiving device may be a network analyzer
or a scalar analyzer. Other possible waveform sampling devices well
known in the art may also be used.
[0072] At block 655, received test waveforms may be sampled. In
some embodiments, a received test waveform may be sampled at a
relatively prime sampling number of times determined at step 625.
When an overall test waveform includes several different separate
waveforms that are based on different frequencies, each separate
waveform may be sampled at a different relatively prime sampling
number in some embodiments. Data acquired from sampling a waveform
may be recorded and stored on a device. In some embodiments, the
device may be a computer, a network analyzer, a scalar analyzer, or
any other device capable of recording and storing data from a
waveform sampling device or component.
[0073] At block 660, a resulting waveform may be created using
interleaving. By interleaving a relatively prime number of samples
of a test waveform, a representation of a base waveform may be
produced. In some embodiments, interleaving of a test waveform
produces in effect a sampling of a base waveform of the test
waveform at an effective sampling rate equal to a product of a
cycle number determined at block 615 and a sample rate determined
at block 610. Merely by way of example, interleaving may be
achieved in some embodiments by determining an integer position in
a data array using the following equation:
Position = Truncate ( MNOP .times. FractionalPart ( Sample_Position
.times. Cycle_Number MNOP ) ) , ##EQU00008##
where MNOP is Minimum Number of Points (or in some embodiments a
relatively prime number of samples), sample position is a number
presenting the position of a sample of the waveform, and cycle
number is the number of cycles within the waveform being sampled.
The truncate function may eliminate the fractional part of a
number, leaving the remaining integer part of the number. The
fractional part function may eliminate the integer part of a number
leaving the remaining fraction part of the number.
[0074] Embodiments may also include methods for sampling a waveform
with a waveform receiving or sampling device in general using
relatively prime based sampling techniques. An overview of
embodiments suitable for methods involving relatively prime
sampling with a waveform receiving or sampling device is provided
in the flow diagram of FIG. 7.
[0075] At block 750, waveforms may be received by a waveform
receiving or sampling device. In some embodiments, the test
waveforms may be received by a sound card. In some embodiments, a
waveform sampling device may be an analog-to-digital converter
("ADC"). In some embodiments, a waveform sampling device may be a
network analyzer or a scalar analyzer. Other possible waveform
sampling devices well known in the art may also be used.
[0076] At block 755, received waveforms may be sampled. A received
waveform may be sampled at a relatively prime sampling number of
times using a waveform sampling device. When an overall waveform
includes several different separate waveforms that are based on
different frequencies, each separate waveform may be sampled at a
different relatively prime sampling number. In some embodiments,
data acquired from sampling a test waveform may be recorded and
stored on a device, such as a computer with a memory, a network
analyzer, a scalar analyzer, or other devices.
[0077] At block 760, a resulting waveform may be created using
interleaving. By interleaving a relatively prime number of samples
of a waveform, a representation of a base waveform may be produced.
In some embodiments, interleaving of a waveform produces in effect
a sampling of a base waveform of the test waveform at an
effectively sampling rate equal to a product of a cycle number and
a sample rate. Merely by way of example, in some embodiments,
interleaving may be achieved by determining an integer position in
a data array using the following equation:
Position = Truncate ( MNOP .times. FractionalPart ( Sample_Position
.times. Cycle_Number MNOP ) ) , ##EQU00009##
where MNOP is Minimum Number of Points (or in some embodiments a
relatively prime number of samples), sample position is a number
presenting the position of a sample of the waveform, and cycle
number is the number of cycles within the waveform being
sampled.
[0078] One skilled in the art will also recognize that the methods
taught within FIG. 6 and its accompanying text also teach methods
for generating waveforms using a waveform generating device
suitable for relatively prime sampling methods in general. Some
embodiments, thus, do not require that the waveform be transmitted
to a DUT, but rather may be used for other purposes where waveforms
may be used.
[0079] In some embodiments, the waveform being received by a
waveform receiving or sampling device may be dithered. For some
embodiments, dithering a waveform may include adding random noise
to each sample of the waveform. In some embodiments, dithering may
be an intentionally applied form of noise, used to randomize
quantization error, thereby preventing large-scale patterns such as
contouring that are more objectionable than uncorrelated noise.
[0080] In some embodiments, the sampled waveform may be fitted
using least square fitting techniques well known in the art.
Systems
[0081] An overview of embodiments suitable for sampling a waveform
using relatively prime sampling techniques is provided in the
structural diagrams of FIGS. 8A, 8B, and 8C. These figures
represent embodiments involving a variety of apparatuses, devices,
and systems suitable for sampling a waveform using relatively prime
sampling techniques. One skilled in the art would also recognize
there are numerous ways to configure apparatuses and systems to
achieve embodiments within the spirit of the invention.
[0082] FIG. 8A provides an embodiment involving a computer 810,
connectors 815 and 816, and a DUT 840. Connector 815 may be
configured to connect with computer 810 to DUT 840 such that a
waveform may be transmitted to DUT 840. Connector 816 may be
configured to connect DUT 840 with computer 810 such that a
waveform that has passed through DUT 840 may be transmitted to
computer 810 where the waveform may be sampled using relatively
prime based sampling methods. One skilled in the art will recognize
there are numerous ways to connect computer 810 with DUT 840.
Merely by way of example, numerous connectors are more thoroughly
discussed in co-pending application U.S. patent application Ser.
No. 12/337,317 filed on Dec. 17, 2008 by Valenti and entitled
"Personal Computer Based Audio Frequency Impedance Analyzer."
Further details regarding computer 810 may be found within FIG. 10
and its accompanying text.
[0083] FIG. 8B provides an embodiment involving a computational
device 820, such as a computer, connectors 825, 826, 861, 862, 871,
and 872, a Z box 850, and a DUT 841. Merely by way of example,
co-pending application U.S. patent application Ser. No. 12/337,317
filed on Dec. 17, 2008 by Valenti and entitled "Personal Computer
Based Audio Frequency Impedance Analyzer" more thoroughly describes
embodiments involving Z box 850. In general, computational device
820 may be connected with Z box 850 to carry waveforms from a sound
card within computational device 820 to Z box 850, which may then
be transmitted to DUT 841 through connector 861 and/or connector
862. Connector 871 and/or connector 872 may then carry a waveform
that has passed through DUT 841 back to Z box 840, from where the
waveform may be transmitted through connector 826 back to
computational device 820. As discussed more thoroughly in
co-pending application U.S. patent application Ser. No. 12/337,317
filed on Dec. 17, 2008 by Valenti and entitled "Personal Computer
Based Audio Frequency Impedance Analyzer," a Z box 850 may be
calibrated using different waveforms that are sent to it from
computational device 820. Some of these waveforms may not pass
through DUT 841, but rather through circuitry of Z box 841 for
calibration purposes. Embodiments as in FIG. 8B may be used, as
with other embodiments seen in FIGS. 8A and 8C, to determine
different measures of DUTs, 841, 841, and 842, such as a transfer
function, using relatively prime sampling methods.
[0084] FIG. 8C provides embodiments involving an analyzer 830,
connectors 835 and 836, and DUT 842. Connector 835 may be
configured to connect analyzer 830 with DUT to carry waveforms from
analyzer 830 to DUT 842. Connector 833 may be configured to connect
DUT 842 with analyzer 830 to transmit waveforms to analyzer 830 for
sampling using relatively prime sampling methods. In some
embodiments, analyzer 830 may be a network and/or a scalar
analyzer. In some embodiments analyzer 830 may include a function
generator. In some embodiments, analyzer 830 may include a digital
storage oscilloscope. One skilled in the art will recognize that
numerous analyzers may provide the functionality involved with
relatively prime based sampling of waveforms. In some embodiments,
analyzer 830 may receive waveforms while another device produces
the waveform that is transmitted to DUT 842.
[0085] An overview of embodiments suitable for sampling a waveform
using relatively prime sampling techniques is provided in the
diagrams of FIG. 9. This represents embodiments involving a variety
of apparatuses, devices, and systems suitable for sampling a
waveform using relatively prime sampling techniques. One skilled in
the art would also recognize there are numerous ways to configure
apparatuses and systems to achieve the similar results.
[0086] FIG. 9 provides an embodiment involving a system for
sampling a waveform using relatively prime sampling methods. FIG. 9
includes a waveform generating device 930. Waveform generating
device 930 may involve a variety of different devices including,
but not limited to, a sound card, an digital-to-analog convert
("ADC"), a computer, a network analyzer, a scalar analyzer, a
function generator, and/or a digital storage oscilloscope. Waveform
generating device 930 may produce a waveform 910, which may include
a plurality of cycles at a frequency. In some embodiments, the
waveform may include more than one plurality of cycles at a
frequency. Such a waveform may include a first plurality of cycles
at a first frequency and a second plurality of cycles at a second
frequency. Each waveform may be comprised of a plurality of base
waveforms, wherein the waveform includes a plurality of the base
waveforms. FIG. 9 shows that waveform 910 may be transmitted to DUT
950. In some embodiments, waveform 910 may bypass DUT 950 rather
than being transmitted through DUT 950. In some embodiments, a
waveform 920 may emerge from DUT 950 and be transmitted to a
waveform receiving or sampling device 940. In some embodiments,
waveform receiving or sampling device 940 may be the same device as
the waveform generating device 930. Waveform receiving or sampling
device 940 may involve a variety of different devices including,
but not limited to, a sound card, an analog-to-digital converter
("ADC"), a computer, a network analyzer, a scalar analyzer, a
function generator, and/or a digital storage oscilloscope. Waveform
receiving or sampling device 940 may receive waveform 920 and
sample waveform 920 using relatively prime sampling methods as
generally disclosed in this Application.
[0087] Computer 1000 may comprise any device having processing
capability sufficient to sample a waveform in accordance with
embodiments. For example, computer 1000 may comprise a personal
computer, a mainframe, or a laptop, whose mobility makes it
especially convenient. Computer 1000 may be configured to control
each of the components comprised by a Z box is generally disclosed
in co-pending application U.S. patent application Ser. No.
12/337,317 filed on Dec. 17, 2008 by Valenti and entitled "Personal
Computer Based Audio Frequency Impedance Analyzer."
[0088] FIG. 10 provides a schematic illustration of a structural
arrangement that may be used to implement computer 1000 according
to an embodiment. In some embodiments a computer 1000 may represent
a controller or computational device as referenced in this
Application. FIG. 10 broadly illustrates how individual elements of
computer 1000 may be implemented in a separated or more integrated
manner. Computer 1000 is shown comprised of hardware elements that
are electrically coupled via bus 1026, including a processor 1002,
an input device such as a waveform receiving and/or sampling
device(s) or component(s) 1004, an output device such as a waveform
transmitting and/or generating device(s) or component(s) 1006, a
storage device 1008, a computer-readable storage media reader
1010a, a communications system 1014, a processing acceleration unit
1016 such as a digital signal processor or special-purpose
processor, and a memory 1018. The computer-readable storage media
reader 1010a is further connected to a computer-readable storage
medium 1010b, the combination comprehensively representing remote,
local, fixed, and/or removable storage devices plus storage media
for temporarily and/or more permanently containing
computer-readable information. The communications system 1014 may
comprise a wired, wireless, modem, and/or other type of interfacing
connection and permits data to be exchanged with external devices
as desired.
[0089] Computer 1000 also may comprise software elements, shown as
being currently located within working memory 1020, including an
operating system 1024 and other code 1022, such as a program
designed to implement different embodiments. For example, computer
1000 may include device drivers for operating and controlling audio
card, sound card, analog-to-digital converter, or digital-to-analog
converter, or more generally, a waveform receiving device and/or a
waveform generating or transmitting device. In addition, computer
1000 may utilize digital signal processing software elements.
Memory 1018 may also include waveform generating code 1025,
waveform receiving code 1027, and waveform processing code 1028.
Furthermore, computer 1000 may comprise software elements designed
to allow a user to input parameters of interest in studying the
response of a DUT to a signal from waveform generating or
transmitting device 1006. Computer 1000 may also include software
elements designed to facilitate analyzing signals received from
calibration and testing of a DUT in order to determine different
measures of a DUT. It will be apparent to those skilled in the art
that substantial variations may be made in accordance with specific
requirements. For example, customized hardware might also be used
and/or particular elements might be implemented in hardware,
software (including portable software, such as applets), or both.
Further, connection to other computing devices such as network
input/output devices may be employed. Connections between the
computer 1000 and various components of a Z box as disclosed in
co-pending application U.S. patent application Ser. No. 12/337,317
filed on Dec. 17, 2008 by Valenti and entitled "Personal Computer
Based Audio Frequency Impedance Analyzer" may use any suitable
connection, such as a parallel-port connection, a
universal-serial-bus ("USB") connection, and the like.
[0090] In some embodiments, waveform receiving and/or sampling
device 1004 may comprise an analog-to-digital converter ("ADC"). In
some embodiments, waveform transmitting device 1006 may comprise a
digital-to-analog convert ("DAC"). In some embodiments, waveform
receiving/sampling device 104 and waveform transmitting/generating
device 1006 may comprise a sound card. A sound card may comprise a
computer expansion card that facilitates the input and output of
audio signals to and from computer 1000 under control of computer
programs. In some embodiments, a sound card may provide the audio
component for multimedia applications such as music composition,
editing video or audio, presentation/education, and entertainment
(games). In some embodiments, computer 1000 may have sound
capabilities built in, while in other embodiments, computer 1000
may require additional expansion cards to provide for audio
capability. In some embodiments, waveform transmitting/generating
device 1006 and/or waveform receiving/sampling device 1004 may come
already installed on computer 1000 when it is purchased. In some
embodiments, waveform transmitting/generating device 1006 and/or
waveform receiving/sampling device 1004 may be installed after
purchases of computer 1000. Waveform transmitting/generating device
1006 and/or waveform receiving/sampling device 1004 may connect up
to computer 1000 in many ways, including but not limited to the
following examples: PCI, ISA, USB, IEEE 1394, Parallel Port, PCI-E,
or PCMIA connections. In some embodiments, sound card 110 may be
directly integrated into computer 100. Waveform
transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may provide an output and input
connection with different configurations as discussed throughout,
including for example, but not limited to, TRS, RCA, and or DIN
connectors. Waveform transmitting/generating device 1006 and/or
waveform receiving/sampling device 1004 may send output signals
over a wide range of frequencies. For example, in some embodiments,
waveform transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may be capable of transmitting and
receiving respectively frequencies ranging from 20 Hertz to 20,000
Hertz. Other embodiments of waveform transmitting/generating device
1006 and/or waveform receiving/sampling device 1004 may have higher
and lower ranges. In some embodiments, waveform
transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may have a lower range such as 5
Hertz, while other embodiments may have a high range, such as
100,000 Hertz, or even higher such as 1 Megahertz. Waveform
transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may produce and sample input signals
respectively at a variety of sizes and rates. In some embodiments,
waveform transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may produce and sample using 8 or 16
bit samples. In other embodiments, the bit sample size might be
higher or lower, such as 32 bit samples for example. Merely by way
of example, in some embodiments, waveform transmitting/generating
device 1006 and/or waveform receiving/sampling device 1004 may
produce and sample signals from about 4000 to 44,000 samples per
second. In some embodiments, waveform transmitting/generating
device 1006 and/or waveform receiving/sampling device 1004 may
produce and sample respectively at higher or lower sampling rates,
such as 48,000 samples per second, merely by way of example. In
some embodiments, waveform transmitting/generating device 1006
and/or waveform receiving/sampling device 1004 may send and/or
receive mono signals. In some embodiments, waveform
transmitting/generating device 1006 and/or waveform
receiving/sampling device 1004 may send and/or receive stereo
signals. In some embodiments, waveform transmitting/generating
device 1006 and/or waveform receiving/sampling device 1004 may
cover different ranges, sizes, rates, or other characteristics from
each other.
[0091] Having described several embodiments, it will be recognized
by those of skill in the art that various modifications,
alternative constructions, and equivalents may be used without
departing from the spirit of the invention. Accordingly, the above
description should not be taken as limiting the scope of the
invention, which is defined in the following claims.
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